Hi, I am doing up my homework on mathematics and here are some questions. I want to cross-reference my answers thank you. Decide if the statements below are True or False. Please include some rough workings for me to understand:

(1) Mr. Tan borrowed $500,000 from Bank XYZ at 5% annual interest to be repaid monthly over 20 years. The amount that he pays back to XYZ each month is between $3000 to $3500.

(2) Continuing from (1): after 15 years, Mr. Tan still owing the bank between $120,000 to $160,000.

(3) 8 persons can sit at a round table with 10 seats 9!/2 ways.

(4) 8 persons sit at a round table with 10 seats so that there is exactly one person between the two empty seats in 8! ways.

(5) On a square grid, you are allowed to go only east (i.e., horizontally to the right) or north (i.e., vertically upwards), moving 1 step at a time. The number of ways (i.e., the number of such paths) by which you can go from (3,3) to (5,5) is8 3.

(6) The number of ways in which 10 identical red balls and 7 identical blue balls can be arranged in a line is17 7.

(7) The sumP2019 k=0 2k is an even number.

(8) According to Benfords law, the probability of 5 being the leading digit of a long list of positive integers (such as the population of various cities) is 0.0969 (to 4 decimal places).

(9) Three fair dice are thrown. The expected value of the total score obtained is 10.5

(10) If the expected number of heads in 5 independent tosses of a coin is 3, then the coin must be fair.

Explain how you will use information from sections in Chapter 2 of a dissertation (Background to the Problem, Theoretical Foundations, and topics in the Review of the Literature) to develop a first draft of Chapter 3 including the Problem Statement, Research Questions, Research Design, Data Collection sources, and Data Analysis. How will you self-score each section using the criteria to help improve the quality of your work and speed up the process of writing your proposal?

An emergency service wishes to see whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period. The data are shown. Emergency Calls and Temperatures Temperature x 68 74 82 88 93 99 101 No. of calls y 7 4 8 10 11 9 13

a. Describe the linear relationship between the temperature and the number of calls.

b. Calculate the correlation coefficient, r.

c. Is r statistically significant at the 0.05 level. Explain.

d. Determine the equation of the line of best fit.

e. Calculate and interpret the coefficient of determination, 2 r .

f. Predict the number of calls when the temperature is 80degrees.

g. Predict the temperature outside when the number of calls is 6.

h. Predict the number of calls when the temperature is 59 degrees

1. A farmer uses a greenhouse to grow his fruits and vegetables year round. He recently purchased a machine that uses artificial intelligence to adjust the lighting to optimize plant growth. He wants to cut down on his energy costs so he started experimenting with two different light bulbs (HID & LED). The farmer would note down the daily kW usage when either is installed that day, each independent of the other. He randomly selected usage data and created the table below. Due to some technical issue, he lost the files containing some values for the LED lighting. Does the data provide sufficient evidence, at α = 0.10, to indicate that average kW usage is lower for the LED bulbs?

Your authors present terms that are used in theory construction. Some of those terms are concepts, variables, statements and hypotheses. Explain how those words are related to one another.

Use a specific theory to illustrate the relationship. In other words, identify a theory; from that theory identify a concept and variables. From those variables develop a statement and a hypothesis.

A survey was conducted to determine, on average, how long patients have to wait to see a doctor. The number of patients that ended up waiting up to 2 hours to see a doctor, recorded in 10-minute intervals, is given in the table below.
a) Define and name the random variable associated with this data.
b) Find the probability distribution for the random variable and draw the corresponding histogram. Express all probabilities as a fraction in lowest terms.
c) What is the probability that a patient had to wait between 20 and 50 minutes?
d) What is the expected number of minutes a patient must wait? Give an exact answer. (2 marks

e) Calculate the standard deviation for this distribution. Explain what it means in the context of this problem.
2.

Waiting Time in minutes
10
20
30
40
50
60
70
80
90
100
110
120 Frequency of Occurrence
1
4
15
20
35
42
28
19
13
5
2
1
e) Calculate the standard deviation for this distribution. Explain what it means in the context of this problem.

Seedlings of the parasitic plant Cuscuta pentagona (dodder) hunt by directing growth preferentially toward nearby host plants. To investigate the possibility that the parasite detects volatile chemicals produced by host plants, a researcher placed individual dodder seedlings into a vial of water at the center of a circular paper disc. A chamber containing volatile extracts from tomato (a host plant) was placed at one edge of the disc, whereas a control chamber containing only solvent was placed at the opposite end. The researcher divided the disk in to 4, equal-area quadrats to record which direction the seedlings grew. 30 dodder plants were tested, and 17 grew toward the volatiles, 2 grew away from the volatiles (toward the solvent), 7 grew toward the left quadrant, and 4 grew toward the right quadrant.

1) Is this an experimental or observational study?

2) State null and alternative hypothesis

3) Which test is appropriate for this study? T-test, contingency test or goodness of fit?

According to the “Bottled Water Trends for 2014” report (bit.ly/1gx5ub8), the U.S. per capita consumption of bottled water in 2013 was 31.8 gallons. Assume that the per capita consumption of bottled water in the United States is approximately normally distributed with a mean of 31.8 gallons and a standard deviation of 10 gallons.

PLEASE USE NORMDIST AND NORMINV IN EXCEL

a. What is the probability that someone in the United States con- sumed more than 32 gallons of bottled water in 2013?

b. What is the probability that someone in the United States consumed between 10 and 20 gallons of bottled water in 2013?

c. What is the probability that someone in the United States consumed less than 10 gallons of bottled water in 2013?

d. Ninety-nine percent of the people in the United States consumed less than how many gallons of bottled water?

e) The amount of water consumed by 92% of US population will be between what two values symmetrically distributed around the mean?

Most companies have increased their dependence on computers and software. As a result, more employee time is spent on the telephone with technical support for the software. A sample of 8 times spent on the phone with technical support yielded the following data:

Construct a 98 percent confidence interval estimate of the true mean population time that is spent by employees on the telephone with technical support for the software. Use only the appropriate formula and/or statistical table in your textbook to answer this question. Negative values should be indicated by a minus sign. Report your answers to 2 decimal places, using conventional rounding rules.

Answer: $ _____≤ (Click to select) ≤ $____

#1 Assume that a new interpretation of the frustration aggression hypothesis says that it is not all people who become aggressive when frustrated, but only those who have been brought up in a home where physical punishment is used become aggressive when frustrated. To test this hypothesis, two groups of children are found. One group is brought up in homes where physical punishment is used as a form of discipline. The other group consists of children whose parents chastise them verbally, or remove privileges, but do not actually hit them. The children are all placed in a situation where they are frustrated in the course of play activity. The play situation includes a doll that the children have in their hands at the time of the frustration experience. The experimenter intends to have judges classify the children as either physically aggressive or not, physically aggressive toward the doll (at the time of frustration). Which statistic would be used?

#2 A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×3 matrix of categories. Which test has the larger value for df?

#3 A chi-square test for independence is being used to evaluate the relationship between two variables. If the test has df = 2, what can you conclude about the two variables?

#4 Under what circumstances will the chi-square test for goodness of fit produce a large value for the chi-square?

#5 For the chi-square test for goodness of fit, the researcher must select a sample with an equal number of individuals in each category.

True

False

#6 A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×2 matrix of categories. Which test has the larger value for df?

#7 What is referred to by the term expected frequencies?

#8 The observed frequencies for a chi-square test can be fractions or decimal values.

True

False

#9 The expected frequencies for a chi-square test are always whole numbers (no fractions or decimals).

True

False

#10 For a chi-square test, the observed frequencies are obtained from the sample.

True

False

#11 A researcher used a sample of n = 60 individuals to determine whether there are any preferences among four brands of pizza. Each individual tastes all four brands and selects his/her favorite. If the data are evaluated with a chi-square test for goodness of fit using α = .05, then how large does the chi-square statistic need to be to reject the null hypothesis?

#12 In general, a large value for chi-square indicates a good fit between the sample data and the null hypothesis.

True

False

#13 A chi-square test for independence is used to evaluate the relationship between two variables. If both variables are classified into 2 categories, then what is the df value for the chi-square statistic?

#14 For the expected frequencies in a chi-square test for independence, the proportions for any row are the same as the proportions in every other row.

True

False

#15 ​ Which of the following best describes the possible values for a chi-square statistic?

Ten females were divided into two equal groups. One group was taught how to concentrate on their breathing (a breathing meditation). A second group was told to imagine that the day was very hot and that they would be allowed to place their hand in cool water. Both groups placed their right hand in buckets of ice water for three minutes. Afterward, they rated their pain on a scale of one to seven (with seven meaning intense pain). Analyze the data and conclude whether the any of the methods was effective in reducing pain.

A. What is the dependent variable?
B. What is the null and alternate hypothesis?
C. Calculate t and note the critical values
D. Calculate d
E. Write your results and interpretations with appropriate stat notations.

Breathing Meditation       Imagination

                             3                         4

                             2                         5

                             4                         7

                             3                         6

                             2                         6

At a certain coffee​ shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 330 cups and a standard deviation of 23 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 170 doughnuts and a standard deviation of 13. Complete parts​ a) through​ c).

Question: The shop is open every day but Sunday. Assuming​ day-to-day sales are​ independent, what's the probability​ he'll sell over 2000 cups of coffee in a​ week? _____________ (round to three decimals as needed.)

Question: Whats the probability that on any given day he'll sell a doughnut to more than half of his coffee customers ? ___________ (round to three decimal places as needed).

A. The data below represent a random sample of 9 scores on a statistics quiz. (The maximum possible score on the quiz is 10.) Assume that the scores are normally distributed with a standard deviation of 1.6. Estimate the population mean with 93% confidence. 6,10,6,4,5,7,2,9,6 6 , 10 , 6 , 4 , 5 , 7 , 2 , 9 , 6 Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

B. Among the most exciting aspects of a university professor's life are the departmental meetings where such critical issues as the color the walls will be painted and who gets a new desk are decided. A sample of 20 professors was asked how many hours per year are devoted to such meetings. The responses are listed below. Assuming that the variable is normally distributed with a standard deviation of 6 hours, estimate the mean number of hours spent at departmental meetings by all professors. Use a confidence level of 90%.

7,11,11,10,17,5,4,9,19,14,4,1,22,10,15,21,17,3,18,16

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

The daily exchange rates for the​ five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.814 in currency A​ (to currency​ B) and standard deviation 0.035 in currency A. Given this​ model, and using the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more​ precisely, complete parts​ (a) through​ (d).

Question: ​a) What would the cutoff rate be that would separate the highest 2.5​% of currency​ A/currency B​ rates? The cutoff rate would be ___________ (type an integer or a decimal rounded to the nearest thousandth as needed)

Question: What would the cutoff rate be that would separate the highest 50% ? The cutoff rate would be _______________

Question: What would the cutoff rate be that would separate the middle 68% ? The lower cutoff rate would be ____________

Question: The upper cutoff rate would be ? ____________________

Question: What would the cutoff rate be that would separate the highest 16%? ________________